-Is there a difference between Excess of Loss and Stop Loss Reinsurance?
Stop loss is a type of excess of loss reinsurance along with catastrophe reinsurance. To elaborate..
Stop loss involves the reinsurer paying the net loss over a retention limit (usually subject to a cap) which arises on a portfolio of contracts over a certain period.
Simple example would be having 10,000 term assurances with SA 1,000. The retention may be set at say 3000. If 10 claims are made then the insurer will receive 7000 from the reinsurer. If 3 (or less) claims are made then the insurer will receive nothing from the reinsurer.
Catastrophe reinsurance would have to involve a catastrophic event (as defined in the treaty). It works in a similar way to stop loss (in that the reinsurer will pay the net amount of any loss over the retention limit) but only if a catastrophic event occurs. A catastrophe could be something like several insured lives dying in the same incident.
-Why is individual surplus reinsurance useful for random fluctuations risk?
Individual surplus can be used when there are a few large policies in a portfolio which result in concentration risk. Section 1.2 of chapter 26 gives a very simple example.
Individual surplus limits the amount of any one payout. It therefore takes the sting out of any particularly large claims. If you had 100 identical, independent policyholders, 99 of which had a SA of 100 and 1 of which had a SA of 100,000 the loss experienced if the single large policy makes a claim is much larger than that if a single small policy makes a claim.
If you had individual surplus reinsurance with a retention of 100 then the loss on the death of any policy holder would be 100 and the loss is no longer dependent on which PH randomly dies.
Open to any corrections, hope this helps.
